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Existence and stability of periodic orbits of periodic difference equations with delays
(World Scientific Publishing, 2008)
In this paper, we investigate the existence and stability of periodic orbits of the p-periodic difference equation with delays xₙ = f(n - 1, xₙ₋ₖ). We show that the periodic orbits of this equation depend on the periodic ...
A new characterization of periodic oscillations in periodic difference equations
In this paper, we characterize periodic solutions of p-periodic diﬀerence equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the ...
An Extension of Sharkovsy’s Theorem to Periodic Difference Equations
We present an extension of Sharkovsky’s Theorem and its converse to periodic difference equations. In addition, we provide a simple method for constructing a p-periodic difference equation having an r-periodic geometric ...
Periodic Orbits in Periodic Discrete Dynamics
We study the combinatorial structure of periodic orbits of nonautonomous difference equations 𝒳ₙ₊₁ = 𝒇ₙ(𝒳ₙ) in a periodically fluctuating environment. We define the Ӷ-set to be the set of minimal periods that are not ...